The Solution Equivalence to General Models for the RIM Quantifier Problem

Hong investigated the relationship between the minimax disparity minimum variance regular increasing monotone (RIM) quantifier problems. He also proved the equivalence of their solutions to minimum variance and minimax disparity RIM quantifier problems. Hong investigated the relationship between the minimax ratio and maximum entropy RIM quantifier problems and proved the equivalence of their solutions to the maximum entropy and minimax ratio RIM quantifier problems. Liu proposed a general RIM quantifier determination model and proved it analytically by using the optimal control technique. He also gave the equivalence of solutions to the minimax problem for the RIM quantifier. Recently, Hong proposed a modified model for the general minimax RIM quantifier problem and provided correct formulation of the result of Liu. Thus, we examine the general minimum model for the RIM quantifier problem when the generating functions are Lebesgue integrable under the more general assumption of the RIM quantifier operator. We also provide a solution equivalent relationship between the general maximum model and the general minimax model for RIM quantifier problems, which is the corrected and generalized version of the equivalence of solutions to the general maximum model and the general minimax model for RIM quantifier problems of Liu’s result

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum

Proceedings of the 11th Workshop on Nonmonotonic Reasoning

These are the proceedings of the 11th Nonmonotonic Reasoning Workshop. The aim of this series is to bring together active researchers in the broad area of nonmonotonic reasoning, including belief revision, reasoning about actions, planning, logic programming, argumentation, causality, probabilistic and possibilistic approaches to KR, and other related topics. As part of the program of the 11th workshop, we have assessed the status of the field and discussed issues such as: Significant recent achievements in the theory and automation of NMR; Critical short and long term goals for NMR; Emerging new research directions in NMR; Practical applications of NMR; Significance of NMR to knowledge representation and AI in general